๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

The computer construction of matrix representationsof finite groups over finite fields

โœ Scribed by R.A. Parker; R.A. Wilson

Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
517 KB
Volume
9
Category
Article
ISSN
0747-7171

No coin nor oath required. For personal study only.

โœฆ Synopsis

Given an abstract group G it is important to be able to find explicit generators for a concrete group isomorphic to G, in order to perform calculations with the group. In this paper we describe a method of using the "Meat-axe" to construct explicit matrix generators for a given group.

๐Ÿ“œ SIMILAR VOLUMES

Groups of Permutation Polynomials over F
Groups of Permutation Polynomials over Finite Fields
โœ Richard M. Stafford ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 195 KB

Let F be a finite field. We apply a result of Thierry Berger (1996, Designs Codes Cryptography, 7, 215-221) to determine the structure of all groups of permutations on F generated by the permutations induced by the linear polynomials and any power map which induces a permutation on F.

Invariants of Finite Groups over Fields
Invariants of Finite Groups over Fields of Characteristicp
โœ David R. Richman ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 578 KB

Let V denote a finite-dimensional K vector space and let G denote a finite group of K-linear automorphisms of V. Let V m denote the direct sum of m copies of V and let G act on the symmetric algebra K[V m ] of V m by the diagonal action on V m . A result of Noether implies that, if char K=0, then K[

Constructing matrix representations of f
Constructing matrix representations of finitely presented groups
โœ S.A. Linton ๐Ÿ“‚ Article ๐Ÿ“… 1991 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 777 KB

The Todd-Coxeter coset enumeration algorithm is one of the most important tools of computational group theory. It may be viewed as a means of constructing permutation representations of finitely presented groups. In this paper we present an analogous algorithm for directly constructing matrix repres